Question

A ray is incident from glass on the boundary separating glass and water. Refractive index for glass is $\frac{3}{2}$ and refractive index for water is $\frac{4}{3}$. The critical angle for the glass-water boundary is

• A. ${\sin }^{-1}\left(\frac{3}{4}\right)$
• B. ${\sin }^{-1}\left(\frac{2}{3}\right)$
• C. ${\sin }^{-1}\left(\frac{8}{9}\right)$
• D. ${\sin }^{-1}\left(\frac{1}{9}\right)$

Answer 1

The correct option is C ${\sin }^{-1}\left(\frac{8}{9}\right)$

Given:
Refractive index of glass (Denser medium), ${\mu }_d=\frac{3}{2}$
Refractive index of water (Rarer medium), ${\mu }_r=\frac{4}{3}$
From formula,
$i_c={\sin }^{-1}\left(\frac{{\mu }_r}{{\mu }_d}\right)$
$\Rightarrow i_c={\sin }^{-1}\left(\frac{4/3}{3/2}\right)$
$\Rightarrow i_c={\sin }^{-1}\left(\frac{8}{9}\right)$